Wednesday, November 07, 2007

Got a whole bunch of good questions from former students. Here's a couple more.

Soul Searcher asks a number of questions. Here's one,

What is the best way to combat grade inflation? I'm teaching a course (first semester organic) right now for 265 undergraduates. Traditionally an average score in this course earns you a B+. Even more ridiculously, based on the last three years, being two standard deviations below the mean will generally earn you a C. There is no such thing as a D (or failure), assuming you sit for one (of three) midterms and the final.

Best way to combat grade inflation? Teach logic.

There's much hand wringing in the academy these days over grade inflation. There's all kinds of evidence that average grades are going up. Is this a question of students getting smarter? Unlikely. Are they coming up through a testing culture where what they've really learned is how to beat assessments? Maybe. Are faculty grading easier in order to appease students and keep them out of their offices so they can do their "real work"? Likely part of the conversation. Are profs trying to give their people an extra little boost to help them get into grad schools? Also likely part of the question.

The best way to combat it is by clearly setting out course goals and expectations. I know it sounds like the dreaded edubabble, but by being clear about what skills and understanding students are expected to acquire, you can stick to your guns in testing those proficiencies and understandings.

My real question though is whether there really is something to be concerned about here. Grades are going up, so what? But if they are inflated, they become meaningless. Yeah, but let's be honest, weren't they meaningless to begin with? With the exception of the occasional student looking to go on to grad school, GPA means absolutely nothing. Grades serve one purpose, to give power to the instructor. Maybe we use it to try to coerce students into doing work because we haven't motivated it well enough in the classroom to make them want to learn it, but in the end what does it really mean? Take a random course from your college career and change the grade down a letter grade, much less a +/- interval. Would your lived life now be any different? For all the anxiety over grade inflation, I wonder whether it's really just profs worrying that they are making our weapon less effective because for some of us, that's all we have in trying to gain respect from students.

Soul Searcher's second question was,

What is the basis of the baseball rule that requires a batter to be tagged out if he/she strikes out and the catcher drops the pitch? What does this rule accomplish? I can see the logic behind the fourth out rule. I can also understand the infield fly rule. However, I have no idea why a batter is not out until tagged when first base is open and the catcher drops the third strike pitch.

The rule does seem odd in that once the batter swings and misses, his turn at bat should be over, yet play continues beyond the strike. It is odd to think the ball is still in play after the whiff, although the foul tip is still in play with two strikes and the catcher holding it is sufficient for a strike out, too. Yet, it is only with two strikes that the ball is live if it gets away from the catcher, the batter only becomes a base runner after he is seemingly out and not before. Yeah, sporting rules are arbitrary, but generally there is a coherent logic to them. I'm with you that this seems a bit bizarre.

Jeff Maynes asks,

In the semantic view of theories, how are we take the word "model"? Set theoretically? If so, what advantages does that give us over the syntactic view?

The semantic view of theories is a position that derived from Bas van Fraassen's constructive empiricism in the 80s and was championed by a number of really smart philosophers of science like Nancy Cartwright, Patrick Suppes, Frederick Suppe, who argued that the traditional view of scientific theories as sets of sentences that were individually testable or testable as a group was wrongheaded. Science is not about finding true statements about the world, but about finding models that fit well and scientific theories were to be thought of, not as set of true or false propositions, but as sets of models. Better theories represent the natural system better, but it becomes a question of usefulness, not of correspondent truth.

So, the question is what is meant by "model," a very ambiguous term. There is the technical sense in logic in which a model is a set of sentences that satisfy an axiom set. There is the sense of model, as in model car, which is a representation of a different scale. There is the sense of a fashion model, an idealized image, someone who wears clothes and looks better in them than you will but you buy them hoping to approximate what you've seen. There are computer models, which are partial specifications of operative factors designed to see what would happen if those were the only aspects of the system. I think that semantic theorists play off of all of these senses. Here's Ronald Giere, one of the major names associated with the semantic view from his book Explaining Science,

I propose that we regard the simple harmonic oscillator and the like as abstract entities having all and only the properties ascribed to them in the standard texts. The distinguishing feature of the simple harmonic oscillator, for example, is that it satisfies the force law F = -kx. The simple harmonic oscillator, then, is a constructed entity. Indeed, one could say that the systems described by the various equations of motion are socially constructed entities. They have no reality beyond that given to them by the community of physicists.I suggest calling the idealized systems discussed in mechanics texts “theoretical models” or, if the context is clear, simply “models.” This suggestion fits well with the way scientists themselves use this (perhaps overused) term. Moreover, this terminology even overlaps nicely with the usage of logicians for whom a model of a set of axioms is an object, or a set of objects, that satisfies the axioms. As a theoretical model, the simple harmonic oscillator, for example, perfectly satisfies its equations of motion.The relationship between some (suitably interpreted) equations and their corresponding model may be described as one of characterization, or even definition. We may even appropriately speak here of “truth.” The interpreted equations are true of the corresponding model. But truth here has no epistemological significance. The equations truly describe the model because the model is defined as something that exactly satisfies the equations.The statements used to characterize models come in varying degrees of abstraction. At its most abstract the linear oscillator is a system with a linear restoring force, plus any number of other, secondary forces. The simple harmonic oscillator is a linear oscillator with a linear restoring force and no others. The damped oscillator has a linear restoring force plus a damping force. And so on. Similarly, the mass-spring oscillator identifies the restoring force with the stiffness of an idealized spring. In the pendulum oscillator, the restoring force is a function of gravity and the length of the string. And so on.

So I think that the logician's notion of a model is not far from mind and in the case of formalizable mathematical models like we see in physical theories, it is exactly what they mean, but I think the idea is kept looser to account for things like scale models in chemistry and computer models.